# Power Spectrum analysis arbitrary length signals

I have signals belonging to diseased and healthy samples recorded from multiple electrodes. These signals are taken monthly and are of arbitrary length (say 4-5 mins). I am planning to do a power spectrum analysis (comparison between healthy and diseased). Now to do this two methods come to mind.

1. Take the normalized power spectrum of the 4/5 min signal as it is and average it over the electrodes.
2. Divide the 4-5 min recordings to smaller (say 5 seconds) segments, obtain the normalized power spectrum of each segment, average it over all the segments, and finally average it over the electrodes.

which of the following methods would give a better analysis?

## 1 Answer

The answer depends on the statistical characterization of the signal. If the random EEG signal is stationary over when seen over 5 second cycles, then you are better off averaging over 5 seconds cycles. If not, then averaging over these 5 seconds cycles might not yield the best estimate. In that case better off averaging over the entire duration.

• Thanks and Sorry I couldn't mention that these signals are Multi-electrode Array signals. When I visualized segment means and variance it seemed that the signals are stationary over time. Even when it's a stationary signal, could you please elaborate on why it's better off averaging over the small cycles rather than considering the whole signal at once. Also am I in the correct path when averaging over the electrodes? Jul 15, 2020 at 11:14
• Because the more you are able to average over samples affected by independent noise, the more accurate the estimate is, in technical terms the varainace of the estimate reduces and it converges to the true value. But the signal samples should be stationary for that to follow, that is why I asked if signal is stationary accross the 5s window Jul 15, 2020 at 11:39
• Regarding averaging over electrodes, if the electrodes are represting similar eeg data then yes, but my understanding is that different electrodes positions should give different eeg patterns (the internal alpha, gamma patterns etc) will vary. So it should be better to do this comparison on per electrode basis and compare electro wise Jul 15, 2020 at 11:41
• Thank you but since these are multi-well electrodes where each well consists of a different culture, we cannot link electrode x in one well to the electrode x in another well. In that case, averaging would make sense right? Jul 17, 2020 at 6:11